fitting a curve (3D) to pointcloud data
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Hello
I have a pointcloud from which I want to extract the border of a street. I have manually created sampling datapoints using the datacursor.
Now I have a list of x, y, z points from which I want to derive a curve (road boarder).
What is the best method of making such a curve given a list of x y z points. It should be smooth.
Thanks for any help!
采纳的回答
Are Mjaavatten
2019-5-20
Assuming that the points are listed in sequence along your curve, you can express x, y, and z as functions of the (approximate) position along the curve, using splines. To illustrate and test, I first generate a set of points to represent your point cloud. The points are randomly distributed along a 3D curve:
t = sort(rand(50,1))*10;
x = sin(t);
y = cos(1.7*t);
z = sin(t*0.22);
plot3(x,y,z,'*')
grid on
Of course, you do not know the parameter t, so we must create a parameter vector s, based on the euclidean distance between points:
s = zeros(size(x));
for i = 2:length(x)
s(i) = s(i-1) + sqrt((x(i)-x(i-1))^2+(y(i)-y(i-1))^2+(z(i)-z(i-1))^2);
end
Now you have x, y, and z as functions of s, and you can generate splines passing through the points:
ss = linspace(0,s(end),100);
xx = spline(s,x,ss);
yy = spline(s,y,ss);
zz = spline(s,z,ss);
hold on
plot3(xx,yy,zz)
hold off
If there is noise in your data and you want to smooth the curve, consider using polyfit / polyval instead of spline.
If your points are not in sequence, the problem gets MUCH harder to automate, and I recommend that you sequence them manually.
5 个评论
Rupert Schaffarz
2019-5-20
Are Mjaavatten
2019-5-20
The best approach would depend on your data, so please attach a file with the data to your original question or to your comment. You can use a *.mat file or a text file.
Rupert Schaffarz
2019-5-20
Are Mjaavatten
2019-5-20
编辑：Are Mjaavatten
2019-5-20
This will work relativey well with your data:
rb = load('road_boarders');
% Right border:
x = rb.right_border_sorted(:,1);
y = rb.right_border_sorted(:,2);
z = rb.right_border_sorted(:,3);
s = zeros(size(x));
for i = 2:length(x)
s(i) = s(i-1) + sqrt((x(i)-x(i-1))^2+(y(i)-y(i-1))^2+(z(i)-z(i-1))^2);
end
px = polyfit(s,x,3);
py = polyfit(s,y,2);
pz = polyfit(s,z,2);
ss = linspace(0,s(end),100);
% Inspect fit:
figure(1);
subplot(3,1,1);plot(s,x,ss,polyval(px,ss));
subplot(3,1,2);plot(s,y,ss,polyval(py,ss));
subplot(3,1,3);plot(s,z,ss,polyval(pz,ss));
figure(2)
plot3(x,y,z,'.r',polyval(px,ss),polyval(py,ss),polyval(pz,ss),'b')
grid on
% Left border:
x = rb.left_border_subset_sorted(:,1);
y = rb.left_border_subset_sorted(:,2);
z = rb.left_border_subset_sorted(:,3);
s = zeros(size(x));
for i = 2:length(x)
s(i) = s(i-1) + sqrt((x(i)-x(i-1))^2+(y(i)-y(i-1))^2+(z(i)-z(i-1))^2);
end
px = polyfit(s,x,3);
py = polyfit(s,y,2);
pz = polyfit(s,z,2);
ss = linspace(0,s(end),100);
figure(3);
subplot(3,1,1);plot(s,x,ss,polyval(px,ss));
subplot(3,1,2);plot(s,y,ss,polyval(py,ss));
subplot(3,1,3);plot(s,z,ss,polyval(pz,ss));
% Both borders in the same plot:
figure(2);
hold on
plot3(x,y,z,'.r',polyval(px,ss),polyval(py,ss),polyval(pz,ss),'b')
axis equal
If the road has more curves, you could try with higher-order polynomials. However, this approach is not likely to handle more than one or two turns. The curve fitting and spline toolboxes have functions for generating smoothed splines, which could probably do the job. I cannot test this, as I do not have access to those toolboxes.
Rupert Schaffarz
2019-5-20
更多回答（3 个）
Amir Suhail
2020-1-1
1 个投票
Hi,
I have similar question. I want to take equdistant points (say N points ) on smooth approximating curve through my data points (x,y,z).
jigsaw
2019-9-21
Are Mjaavatten's answer works great for me. The following lines can be modified a bit to be more concise. Replace the
s = zeros(size(x));
for i = 2:length(x)
s(i) = s(i-1) + sqrt((x(i)-x(i-1))^2+(y(i)-y(i-1))^2+(z(i)-z(i-1))^2);
end
with
s = [0;cumsum(flip(sqrt((x(end:-1:2)-x(end-1:-1:1)).^2+(y(end:-1:2)-y(end-1:-1:1)).^2+(z(end:-1:2)-z(end-1:-1:1)).^2)))];
deb.P
2019-11-8
0 个投票
i have a question: i have fitted a curve to my 3 variable data set according to the code Are Mjaavatten has mentioned. Now i want to know what is the equation of the fitted curve.
1 个评论
Are Mjaavatten
2019-11-9
If you have used the polyfit version, px, py and pz give the coefficients for the fitted polynomials in s. See the docmentation for polyfit for details.
If you used spline, the expressions are piecewise cubic spline polynomials. Se the documentation for spline for details.
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